Journalists and academics have a lot to say about what U.S. judges do and why they do it. Many veteran court-watchers believe that the Supreme Court now is, and has long been, almost equally divided between "conservatives" and "liberals."

Skeptical journalists treat judges as little more than politicians in black robes. Others insist that presidents are routinely disappointed by their appointees and that you just can't predict how judges will vote. For their part, judicial nominees typically declare they will simply follow the law. Chief Justice John Roberts proclaimed that judges are neutral umpires, and Justice Sonia Sotomayor said that "in every case I have decided, I have done what the law requires."

However incompatible, claims of this kind are often made with great conviction, as if nothing could be more obvious. But they tend to be based on vague impressions and isolated examples. In recent years, those who study federal courts have started to test these claims by analyzing many thousands of judicial votes. Armed with actual data, the researchers are finding that much of the conventional wisdom is wrong, or at least way off.

Judges are far from mere politicians; we don't see anything like the kind of polarization found in Congress. At the same time, judicial predispositions matter, and they help explain why judges are divided on some of the great issues of the day. We also have reason to think that no fewer than three of the current justices are among the most conservative since the 1930s - and that none of the current justices ranks among the most liberal.

It is easiest to investigate the federal courts of appeals, which decide cases in three-judge panels. With a little counting (OK, a lot), we can see how Republican and Democratic appointees vote in politically contested areas, such as affirmative action, gay rights, abortion, campaign-finance regulation, disability discrimination, sexual harassment and environmental protection. We can examine how often Republican and Democratic appointees cast stereotypically liberal votes - for example, in favor of affirmative action, gay rights, campaign-finance limits, and people complaining of discrimination.

It turns out that a real difference exists between Republican and Democratic appointees. In the politically contested areas, Republican appointees have been found, over a lengthy recent period, to cast liberal votes about 40 percent of the time, whereas Democratic appointees do so about 52 percent of the time. Crucially, the law matters; a 12-point difference isn't huge. But that difference isn't exactly small. If you want to know how a judge will vote in a case involving affirmative action, sexual harassment or gay rights, the political party of the appointing president is a significant clue.

Second, judicial voting becomes a lot more ideological when judges sit on panels with two others appointed by presidents of the same political party. For example, Republican appointees side with plaintiffs complaining of disability discrimination about 29 percent of the time - but that number drops to 17 percent when they are sitting with two fellow Republican appointees. Here, then, is evidence that federal judges (no less than the rest of us) are subject to group polarization, which exists when like-minded people go to extremes.

Third, judges get far more moderate when they sit on panels with two other judges appointed by presidents of the other political party. When Democratic appointees sit with two Republican appointees, they vote a lot like Republican appointees. When Republican appointees sit with two Democratic appointees, they vote a lot like Democratic appointees. Here is strong evidence of a conformity effect on the federal courts.

The most important federal tribunal, of course, is the Supreme Court. In a new book, political scientist Lee Epstein of the University of Southern California and her co-authors - economist William Landes of the University of Chicago Law School and Richard Posner, a federal judge appointed by President Ronald Reagan - examine the votes of 44 Supreme Court justices since 1937. Strikingly, they find that of the six most conservative justices in their entire sample, no fewer than three are currently on the court (Clarence Thomas, Antonin Scalia and Samuel Alito). A fourth makes the top 10 (John Roberts). By contrast, none of the current justices ranks among the most liberal six, and only one makes the liberal top 10 (Ruth Bader Ginsburg).

On these numbers, the current court is skewed to the right, at least by historical standards. It has three of the most conservative justices in the last 76 years, and they have no liberal counterparts. Epstein and her co-authors also find that Republican presidents - at least since Richard Nixon - have generally succeeded in appointing the more conservative justices, while Democratic presidents have generally succeeded in appointing the more liberal ones.

With only a few exceptions (including John Paul Stevens and David Souter), recent presidents haven't had reason to be surprised by the voting patterns of the people they have appointed to the Supreme Court. At the same time, it is true that some Republican appointees are a lot more conservative than others, and there is also an ideological spectrum on the Democratic side.

To be sure, counting votes hardly tells us everything. Nonetheless, we are learning that some widely held views are off the mark. The good news is that because the law imposes real constraints, Republican and Democratic appointees frequently agree. But justice is not exactly blind. In many important cases, the predispositions of the judges play a significant role in determining the nature of people's legal rights.

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Cass R. Sunstein, the Felix Frankfurter professor of law at Harvard University, is a Bloomberg View columnist. He is the former administrator of the White House Office of Information and Regulatory Affairs, the co-author of "Nudge" and author of "Simpler: The Future of Government," forthcoming in 2013.